Properties of tug-of-war model for cargo transport by molecular motors

Molecular motors are essential components for the biophysical functions of the cell. Current quantitative understanding of how multiple motors move along a single track is not complete, even though models and theories for a single motor mechanochemistry abound. Recently, Müller et al. have developed a tug-of-war model to describe the bidirectional movement of the cargo [Proc. Natl. Acad. Sci. U.S.A. 105, 4609 (2008)]. They found that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested that the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we will carry out a detailed theoretical analysis of a special case of tug-of-war model: in which the numbers of the two different motor species which bound to the cargo tend to infinite. Through the analysis, all the stable, i.e., biophysically observable, steady states and their stability domains can be obtained. Depending on values of the several parameters, the tug-of-war model exhibits uni-, bi-, or tristability. The steady-state movement of the cargo, which is transported by two different molecular motor species, is determined by the initial numbers of the motors which bound to the track.